Amrita School of Engineering, Amrita Vishwa Vidyapeetham - Bengaluru Campus

Being a student from Tier-2 college, I can tell you that the following companies generally come for placements:
-Caterpillar (offered Highest package during my college time )
-Mahindra and Mahindra
-Tata motors
-L&T
-Wheels India
-Bosch
-Suzlon
-Flowserve
-Ucal fuel systems
-Hyundai motors
-Ford India
-Blue Star
- Elgi
Apart from these, there will be software companies for recruitment.

I doubt you can get a seat from counselling. You could try for a management seat.

Yup, you can definitely get a seat in EEE or EIE.

SRM University, Chennai offers better placements for B.Tech and if you want to know the placement about any other branch, then kindly mention it.

Hello Gopa, please use Shiksha compare college: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

VIT, Vellore is better than Amrita, Bangalore as in VIT there is tie-ups with many companies and also some companies have their research incubators where students go for the workshops regularly.

Nope, not even in your bags or else it is likely to get confiscated.